Question

Given is a right triangle with side lengths a, b, and c. The Pythagorean triple (9,12,15) represents the side lengths of the given right triangle. Which of the following is the correct value of a? (1 point) Responses a=15 a equals 15 a=12 a equals 12 a=81 a equals 81 a=9 a equals 9 Skip to navigation

Answer 1

In a right triangle, the side lengths can be labeled as follows: \(a\) and \(b\) are the lengths of the legs, and \(c\) is the length of the hypotenuse. In the Pythagorean triple (9, 12, 15), the longest side, which is the hypotenuse \(c\), is 15. The lengths of the legs \(a\) and \(b\) would therefore be 9 and 12.

Since the question asks for the correct value of \(a\), we can say:

1. If we let \(a = 9\) and \(b = 12\), then it is consistent with the given Pythagorean triple.
2. Alternatively, if we let \(a = 12\) and \(b = 9\), that is also true.

However, based on the options provided, the most commonly accepted value for side \(a\) in this context would be the smallest leg of the triangle.

Thus, the correct value of \(a\) is:

a = 9